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" Things which are equal to the same thing, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal. "
Elements of Geometry and Trigonometry from the Works of A.M. Legendre ... - Page 18
by Charles Davies, Adrien Marie Legendre - 1885 - 512 pages
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1857 - 242 pages
...equal to each other. 2. If equals are added to equals, the wholes are equal. 3. If equals are taken from equals, the remainders are equal. 4. If equals are added to unequals, the wholes are unequal. 5. If equals are taken from unequals, the remainders are unequal. 6. Things which...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 256 pages
...equal to each other. 2. If equals are added to equals, the wholes arje equal. 3. If equals are taken from equals, the remainders are equal. 4. If equals are added to unequals, the wholes are unequal. 5. If equals are taken from unequals, the remainders are unequal. 6. Things which...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1871 - 302 pages
...equal to each other. 2. If equals are added to equals, the wholes are equal. 3. If equals are taken from equals, the remainders are equal. 4. If equals are added to unequals, the wholes are unequal. 5. If equals are taken from unequals, the remainders are unequal. 6. Things which...
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Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 376 pages
...The following are some of the most important axioms and postulates. Axioms. 1°. Things equal to the same thing are equal to each other. 2°. If equals...equals, the remainders are equal. 4°. If equals are multiplied by equals, the products are equal. 5°. If equals are divided by equals, the quotients are...
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New Practical Algebra: Adapted to the Improved Methods of Instruction in ...

James Bates Thomson - Algebra - 1878 - 322 pages
...2 = what ? 15. 26 -r- (x — b) + axbxy + zz = what ? AXIOMS. 59. An Axiom is a self-evident truth. 1. Things which are equal to the same thing, are equal...equals, the remainders are equal. 4. If equals are multiplied by equals, the products are equal. 5. If equals are divided by equals, the quotients are...
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Elements of Plane Geometry

Franklin Ibach - Geometry - 1882 - 208 pages
...in a proposition or in a demonstration. 38. A Scholium is a comment on one or more propositions. 39. AXIOMS. 1. Things which are equal to the same thing...are equal. 8. The whole is greater than any of its parts. 10. Only one straight line can join two points. 11. A straight line is the shortest distance...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 264 pages
...are equal to each other. 2. If equals are added to equals the sums are equal. 3. If equals are taken from equals the remainders are equal. 4. If equals are added to unequals the sums are unequal, arid the greater sura is obtained from the greater magnitude. 5. If equals are taken from unequals...
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Numbers Universalized: An Advanced Algebra, Volume 2

David Martin Sensenig - Algebra - 1890 - 556 pages
...truth. 60. The following are the principal axioms relating to numbers : 1. Things that are equal to the same thing are equal to each other. 2. If equals are...equals the remainders are equal. 4. If equals are multiplied by equals the products are equal. 5. If equals are divided by equals the quotients are equal....
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Elements of Algebra: A Course for Grammar Schools and Beginners in Public ...

William James Milne - Algebra - 1894 - 214 pages
...truth that does not need demonstration is called an Axiom. AXIOMS. 1. Things that are equal to the same thing are equal to each other. 2. If equals are...equals, the remainders are equal. 4. If equals are multiplied by equals, the products are equal. 5. If equals are divided by equals, the quotients are...
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Elements of Algebra: A Course for Grammar Schools and Beginners in Public ...

William James Milne - Algebra - 1894 - 212 pages
...truth that does not need demonstration is called an Axiom. AXIOMS. 1. Things that are equal to the same thing are equal to each other. 2. If equals are...equals, the remainders are equal. 4. If equals are multiplied by equals, the products are equal. 5. If equals are divided by equals, the quotients are...
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